Abstract: Aims: We investigated the X-ray emission from young stars and brown dwarfs inthe sigma Orionis cluster tau~3 Ma, d~385 pc and its relation to mass,presence of circumstellar discs, and separation to the cluster centre by takingadvantage of the superb spatial resolution of the Chandra X-ray Observatory.Methods: We used public HRC-I-Chandra data from a 97.6 ks pointing towards thecluster centre and complemented them with X-ray data from IPC-Einstein,HRI-ROSAT, EPIC-XMM-Newton, and ACIS-S-Chandra together with optical andinfrared photometry and spectroscopy from the literature and public catalogues.On our HRC-I-Chandra data, we measured count rates, estimated X-ray fluxes, andsearched for short-term variability. We also looked for long-term variabilityby comparing with previous X-ray observations. Results: Among the 107 detectedX-ray sources, there were 70 cluster stars with known signposts of youth, twoyoung brown dwarfs, 12 cluster member candidates, four field dwarfs, and twogalaxies with optical-infrared counterpart. The remaining sources hadextragalactic nature. Based on a robust Poisson-chi^2 analysis, nine clusterstars displayed flares or rotational modulation during the HRC-I observations,while other eight stars and one brown dwarf showed long-term X-ray fluxvariations. We constructed a cluster X-ray luminosity function from O9.5 ~18Msol to M6.5 ~0.06 Msol. We found: a tendency of early-type stars inmultiple systems or with spectroscopic peculiarities to display X-ray emission,that the two detected brown dwarfs and the least-massive star are among thesigma Orionis objects with the highest L X-L J ratios, and that a largefraction of known classical T Tauri stars in the cluster are absent in this andother X-ray surveys. We concluded that dozens X-ray sigma Orionis stars andbrown dwarfs are still to be detected abridged.